Uh, Johnson 1968.
All five times, since 1960, that a vice president sought the nomination for president after his party controlled the White House for at least two terms he has gotten it (Richard Nixon in 1960, Hubert Humphrey in 1968, Gerald Ford in 1976, George H.W. Bush in 1988, Al Gore in 2000).
Ford was the incumbent President. Granted not by election, but he was President none-the-less.